This is a three part problem...I need direction on the next two tasks PLEASE its due today!

Question

Task 2: An investor is willing to spend $1,000 to start a business. After selling his items, he wants his total amount earned to be at least three times the amount he originally spent. How much is he hoping for? Determine the price he should sell his items for (he was selling item 1 for $2 and item2 for $3) Write an inequality that represents the fact that he wants his total earned to be three times the amount originally spent. (Be sure to include cost of items) What is the ideal number of items he should produce and sell? Why?

Task3: A customer in Alaska wants to purchase several of these items and wants the owner to ship the items to her. The cost per item is $6.00 (has already been established) and the owner will only charge the customer $5.00 to ship these items to Alaska. Suppose another company sells the same item, but charges half the first company’s price. However, if the customer buys from this company, she will be charged $20 in shipping costs.  Write two equations to represent the customer’s total cost based on how many items she buys from each of the two sellers. If the customer in Alaska wants to buy 5 items, which seller should she buy from? If the customer in Alaska wants to buy 50 items, from which seller should she buy from?

 

Answer 1

If he triples the price of the items the inequality will be 6A+9B>3000 where A is the number of item 1 and B the number of item 2. The total amount earned from sales has to be at least 3*1000=$3000. The first inequality can also be written 2A+3B>1000 reflecting his original investment. The cost of production has not been given. Without it we can't work out or determine the profit. If he produces item 1 only A>500; if he produces item 2 only B>333. Otherwise, A>(1000-3B)/2 or 500-(3/2)B. If B is an even number starting at 0, then B can be written B=2X where X is an integer. Then A>500-3X, so if we write (A,B) we have all possible pairs (500,0), (497,2), (494,4), (491,6), etc. as the numbers of each item. These are the minimum required to earn at least $3000 from sales. The amount of money earned for each pair is $3000. The total number of items for each pair is: 500, 499, 498, 497, etc. There are equal numbers of each item (200,200), 400 items in all, and 200*6+200*9=3000. When B=334 (X=167) and A=0, the total number of items is, of course, 334 which earns $3006.

If the shipping cost is $5 per item, then the cost per item is $11 and the total cost is 11x where x is the number of items. If $5 is the overall shipping cost then the total cost=5+6x. Assume the latter.

The other company's cost per item is $3 (half of $6) and the overall cost is 20+3x.

The Alaskan customer's cost is (a) 5+6x for x items; (b) 20+3x for x items. If x=5 then (a)=35 and (b)=35; if x=50 (a)=$305 and (b)=$170. For 5 items there is no difference in cost, and for 50 items the second company is cheaper.